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FIN 413 – RISK MANAGEMENT. Futures and Forward Markets. Topics to be covered. Spot versus futures transactions Futures trading Cancelling a futures position Convergence of futures and spot prices Operation of margin Making/taking delivery Forward contracts. Suggested questions from Hull.

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Fin 413 risk management
FIN 413 – RISK MANAGEMENT

Futures and Forward Markets


Topics to be covered
Topics to be covered

  • Spot versus futures transactions

  • Futures trading

  • Cancelling a futures position

  • Convergence of futures and spot prices

  • Operation of margin

  • Making/taking delivery

  • Forward contracts


Suggested questions from hull
Suggested questions from Hull

6th edition: #2.1,2.8, 2.11, 2.12, 2.21

5th edition: #2.1,2.8, 2.11, 2.12, 2.21


Futures contract
Futures contract

  • An agreement between two parties (a buyer and a seller) to exchange a specified quantity of an asset (the underlying asset) during a specified future period (the delivery period of the contract) at a specified place for a price (the futures price) agreed to in advance (when the contract is first entered into).


Spot versus futures transaction

Item is exchanged for $.

Agreement is reached.

Item is exchanged for $.

Agreement is reached.

Spot versus futures transaction

Spot transaction:

Now

Futures transaction:

Now

T


Futures trading

Buyer

Long

Seller

Short

Futures contract

Takes delivery.

Makes delivery.

Futures trading


Futures trading1
Futures trading

Organized futures exchanges:

  • CBOT: corn, soybeans, wheat, Treasury bonds, Treasury notes

  • CME: pork bellies, live cattle, live hogs, S&P 500 stock index, foreign currencies, Eurodollars

  • WCE: canola, flaxseed, oats, western barley

  • ME: Canadian government bonds, S&P/TSX Canada 60 index

    Hull, pages 543: URLs of the major exchanges


History

1972: currency futures

1982: stock-index futures

1848: CBOT

1904: WCE

1874: CME

1971: Breakdown of Bretton Woods Accord

1975: interest-rate futures

History

17th century futures market for rice, Japan


Example
Example

  • It is June.

  • Vancouver food processor will require canola in September. Buys 20 metric tons in the futures market.

    • Instructs its broker to buy one futures contract (for the delivery of 20 metric tons of canola) with delivery in September.

    • Broker passes the instructions to the WCE.

    • Instructions are forwarded to a trader on the floor of the exchange.


Example continued
Example (continued)

  • The trader assesses the best price (the lowest price) available. The trader indicates a willingness to buy one September contract at that price.

  • If another trader indicates a willingness to sell at that price, a deal is done.

  • Otherwise, the first trader must signal a willingness to buy at a higher price.

  • Eventually, an agreement will be reached, for example, $387 per metric ton or $7,740 in total.


Example continued1
Example (continued)

  • The trader who agrees to sell canola at $387 per metric ton might represent an Alberta farmer.

  • Both the food processor and the farmer have entered into a legally binding agreement.

  • Futures prices are determined by the forces of demand and supply.

  • Futures prices fluctuate over the life of each contract.

  • At any time, a futures contract has zero value to a prospective buyer or seller.

  • Apart from commissions and bid-ask spreads, a futures contract requires no initial payment or premium. The futures price simply represents the price at which the parties agree today to transact in the future.

  • Futures exchanges offer electronic trading services.


Mechanics of futures trading
Mechanics of futures trading

  • A trader can buy/sell futures through:

    • A full-service futures broker.

    • A discount, online futures broker.

  • Full-service broker:

    • Charges a commission.

    • Executes trades.

    • Provides advice and other services.

    • May provide online trading at reduced rates.

  • Discount broker:

    • Charges a smaller commission.

    • Executes trades and provides fewer other services.


Futures markets
Futures markets

  • Futures contracts trade on organized exchanges.

  • Their terms are standardized with respect to:

    • The underlying asset: the required quality and quantity are specified.

    • Delivery location: where delivery can be made.

    • Delivery period: when delivery can be made.

  • www.wce.ca


Futures markets1
Futures markets

  • Futures exchanges offer the short:

    • The quality option.

    • The delivery option.

    • The timing option.

  • The price charged to the long is adjusted accordingly.

  • If the short notifies the exchange of his/her intention to deliver, the short is matched with the buyer holding the oldest outstanding long position in the contract. The long is notified to take delivery.


The minimum tick

Alberta farmer

Some seller

Transaction 1

$387

Transaction 2

$387.03

$387

Vancouver food processor

Some buyer

The minimum tick

  • The exchange does not want to keep track of price changes smaller than $0.10 per metric tonne (or $2 per contract).


Life of mar08 canola futures contract
Life of Mar08 canola futures contract

F

F1

S

Last trading day:March 14, 2008

S1

1st trading day

t1

Trader takes position in contract

Delivery period

Delivery month:March 2008

Life of contract:About 2.5 years


Question examples
Question & examples

Question: Do farmers use futures contracts?

Examples: #2.8, 2.21


Spot versus futures transaction1

Item is exchanged for $.

Agreement is reached.

Item is exchanged for $.

Item is exchanged for $.

Item is exchanged for $.

Agreement is reached.

Spot versus futures transaction

Spot transaction:

Now

Futures transaction:

Now

T


Spot versus futures transaction during the delivery period
Spot versus futures transaction – during the delivery period

Spot transaction:

Item is exchanged for $.

Now

T

Agreement is reached.

Futures transaction:

Item is exchanged for $.

Now

T

Agreement is reached.


Convergence of f to s

F period

Inverted Market

Normal Market

F

S

S

F

1st trading day

1st trading day

1st trading day

DP

DP

Convergence of F to S

  • Ignore transaction costs.

  • If F > S during the delivery period:

    • Buy the asset for S in the spot market.

    • Short a futures contract.

    • Make delivery, selling the asset for F.

  • Arbitrage profit per unit of underlying asset = (F -S)

  • S rises and F falls.


Convergence of f to s1

F period

Convergence of F to S

Inverted Market

Normal Market

F

S

S

F

1st trading day

1st trading day

1st trading day

DP

DP

  • Ignore transaction costs.

  • If F < S during the delivery period:

    • Go long a futures contract, agreeing to buy the asset at F.

    • Wait for the short to make delivery.

    • Sell the asset in the spot market at the spot price at that time, S*.

  • Profit per unit of underlying asset = (S*-F)

  • F rises and S falls.


Futures price

F periodNov08

FMar08

S

Now

Nov08

Mar08

Futures price

  • At any given time, a number of (canola) futures contracts are trading, identified by their delivery months.

  • Mar08 and Nov08 contracts are trading currently.

  • Assuming a normal market:


Cancelling a futures position
Cancelling a futures position period

  • Futures contract: a legally binding agreement.

  • A position can be easily terminated:

    • Making/taking delivery.

    • Closing out or offsetting.

    • Undertaking an exchange-for-physicals (EFP) transaction.


Offsetting
Offsetting period

Action: Short (sell) five May 2008 cocoa futures

Obligation: Deliver 50 metric tons of cocoa to the buyer in May 2008

Offsetting action: Go long (buy) five May 2008 cocoa futures

Obligation: Zero

Action: Go long (buy) two December 2009 US T-note futures

Obligation: Buy $200,000 worth of US T-notes in December 2009

Offsetting action: Short (sell) two December 2009 US T-note futures

Obligation: Zero


Efp transaction

EFP transaction period:

Trader A

Trader B

Agrees with B to purchase wheat and cancel futures

Agrees with A to sell wheat and cancel futures

Receives wheat and pays B

Delivers wheat and receives payment from A

Reports EFP to the exchange

Reports EFP to the exchange

Exchange cancels A’s long futures position

Exchange cancels B’s short futures position

EFP transaction

Before EFP:


Cancelling a futures position1
Cancelling a futures position period

  • Very few traders (less than 2%) ever take or make delivery on a futures contract:

    • Inconvenient, expensive.

    • Not required to realize the benefits of hedging.

    • Speculators and arbitrageurs only want to trade the contract.


Light sweet crude oil futures
Light sweet crude oil futures period

  • www.nymex.com



Operation of margins
Operation of margins period

  • Margin accounts:

    • Clearinghouse member (with the clearinghouse)

    • Broker (with a CH member)

    • Trader (with a broker)

  • Margin: good faith or security deposit.

  • Initial margin: the initial amount put in a margin account by a trader to establish a futures position.

  • Maintenance margin: the minimum amount that a trader must keep in a margin account to maintain a futures position.


Operation of margins1
Operation of margins period

  • Margin accounts are marked to market daily: they are adjusted daily for net gains/losses realized on a futures position.

  • Trader: at the end of each day, his/her margin account is increased by the amount of the daily gain or reduced by the amount of the daily loss.

  • Broker: his/her margin account is adjusted for daily net gains/losses over the accounts of all of his/her clients.

  • Clearinghouse member: his/her margin account is adjusted daily for net gains/losses over the accounts of all of his/her clients.

  • Purpose of margining system: To reduce credit risk, that is, to reduce the probability of market participants sustaining losses because of defaults.


Operation of margins2
Operation of margins period

  • Daily marking to market is equivalent to:

    • Closing a futures contract at the end of each day.

    • Opening a new contract at the beginning of the next business day with zero value to the trader.


Example1
Example period

A trader buys two November frozen orange juice futures contracts through her broker.

Each contract is for the delivery of 15,000 pounds of orange juice.

F1, the current futures price, is 160 cents per pound.

Initial margin: $6,000 per contract

Maintenance margin: $4,500 per contract

The contract is entered into on September 8 at 160 cents/pound (F1) and closed out on September 14 at 161 cents/pound (F2).


Example continued2
Example (continued) period

1.85

7,500


Gain loss on futures

The long periodgains $-for-$ as F rises.

F1

The long loses $-for-$ as F falls.

The short loses $-for-$ as F rises.

F1

The short gains $-for-$ as F falls.

Gain/loss on futures

The long:

The short:

A futures contract is a zero-sum game.


Gain loss on futures1
Gain/loss on futures period

Example:

Price at beginning of day = F1 = $1.50

Price at end of day = F2 = $1.60

Long’s gain (per unit of UA) on the day = (F2 – F1) = $0.10

Short’s gain (per unit of UA) on the day = (F1 – F2) = -$0.10Long’s gain + short’s gain = 0

Example:

Price at beginning of day = F1 = $1.50

Price at end of day = F2 = $1.30

Long’s gain (per unit of UA) on the day = (F2 – F1) = -$0.20

Short’s gain (per unit of UA) on the day = (F1 – F2) = $0.20Long’s gain + short’s gain = 0


Example continued3
Example (continued) period

1.85

7,500

7,500

19,500

1.70

(4,500)

3,000

15,000

1.35

(10,500)

(7,500)

4,500

7,500

1.56

6,300

(1,200)

18,300

1.56

0

(1,200)

18,300

1.61

1,500

300

19,800

Cumulative gain on September 14 = (F2-F1)×30,000 = ($1.61-$1.60)×30,000 = $300.


Newspaper quotes
Newspaper quotes period

The National Post web site, May 25, 2007:

www.canada.com/national/nationalpost/financialpost/fpmarketdata

CANOLA (WPG)20 metric tons, C$ per metric ton; 10 cents = $2 per contract

Prev. vol. 9,635 Prev. open int. 120,758

Question: Is the market normal, inverted, or mixed?


Making taking delivery
Making/taking delivery period

F1: futures price at the time a position is taken. The trader agrees to buy/sell at this price.

Hull, page 33: “For all contracts the price (received by the short and paid by the long) is usually based on the settlement price immediately preceding the date of the notice of intention to deliver.”

Contradiction?


Making taking delivery1
Making/taking delivery period

T: the business day immediately preceding the date of the notice of intention to deliver

FT: the settlement price at time T

Effective price received by the short:FT + gain on futures= FT + (F1 – F2) + (F2 – F3) + (F3 – F4) … + (FT-1 – FT)= F1

Effective price paid by the long:FT + loss on futures= FT + (F1 – F2) + (F2 – F3) + (F3 – F4) … + (FT-1 – FT)= F1

Note: F1 is paid/received via a sequence of daily instalments over the period the position is held, because of marking to market.


Example2
Example period

  • The benefits of hedging can be realized by closing out a futures position just prior to the delivery period.


Example3
Example period

Notation:

F1: futures price at time position is taken

F2: futures price at time position is closed

S1: Spot price at time futures position is taken

S2: Spot price at time futures position is closed


Example continued4
Example (continued) period

It is June 15.

A hog farmer expects to have 90,000 pounds of hogs to sell at the end of August. To hedge, he shorts three September hog futures contracts, each for the delivery of 30,000 pounds of live hogs.

F1 = $0.75225 per pound

The farmer plans to close out his short futures position on August 26 and to sell his hogs in the spot market at that time.

Note: This strategy will yield the farmer a price for his hogs that is close to $0.75225 per pound.

Consider two cases:

  • S2 = $0.73000 < $0.75225

  • S2 = $0.80000 > $0.75225


Case 1 s 2 f 1

Gain on futures period

Spot price

Case 1: S2 < F1

F1

F2

S1

S2

June 15

August 26

September

Effective price received by the farmer


Case 2 s 2 f 1

Loss on futures period

Case 2: S2 > F1

F2

S2

F1

Spot price

S1

June 15

August 26

September

Effective price received by the farmer


Newspaper quotes1
Newspaper quotes period

The National Post web site, May 25, 2007:

www.canada.com/national/nationalpost/financialpost/fpmarketdata

CANOLA (WPG)20 metric tons, C$ per metric ton; 10 cents = $2 per contract

Prev. vol. 9,635 Prev. open int. 120,758


Hull 2 22 page 43
Hull: #2.22, page 43 period

“When a futures contract trades on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one.”

  • Suppose OI = 65,613A trade takes place:

    A goes long entering into a new contract.

    B goes short entering into a new contract.

    OI = ?

    ΔOI = ?


Hull 2 22 page 431
Hull: #2.22, page 43 period

(b) Suppose OI = 65,613

A trade takes place:

A goes long closing out a previous short position.

B goes short closing out a previous long position.

OI = ?

ΔOI = ?


Hull 2 22 page 432
Hull: #2.22, page 43 period

(c) Suppose OI = 65,613A trade takes place:

A goes long entering into new contract.

B goes short entering into a new contract.

OI = ?

ΔOI = ?

Another trade occurs.

C goes long entering into a new contract.

A goes short closing out the previous long position.

OI = ?

ΔOI?


Open interest

B1 period

B2

B3

$290

$295

$300

S1

S2

S3

Open interest

  • Open interest = 3


Open interest1

B1 period

B2

B3

B4

$290

$295

$300

$298

S1

S2

S3

B3

Open interest

  • A trade takes place:

    B4 goes long entering into a new position

    B3 goes short closing out her previous long position


Open interest2

B1 period

B2

B3

B4

$290

$295

$300

$298

S1

S2

S3

B3

Open interest

  • Open interest = 3

  • B4 is agreeing to buy at $298. S3 is agreeing to sell at $300. But if they take/make delivery, they will exchange the underlying asset at FT.

  • The effective counterparty is the clearinghouse.


Forward contract
Forward contract period

  • An agreement between two parties (a buyer and a seller) to exchange a specified quantity of an asset (the underlying asset) at a specified future time (the delivery date of the contract) for a price (the delivery price) agreed to in advance (when the contract is first entered into).



Delivery price and forward price
Delivery price and forward price period

  • Delivery price:

    • The price specified in a forward contract.

    • Negotiated at inception; makes the contract have zero value to both parties.

    • Doesn’t change over the life of the contract.

  • Forward price:

    • The price that, at any point in time during the life of a contract, makes the contract have zero value to both parties.

    • Changes over the life of the contract.


Forward contract1
Forward contract period

Notation:

K : the delivery price

F : the forward price

S : the spot price of the underlying asset

f : the value of the contract to the long

-f : the value of the contract to the short

Note: A forward contract is a zero-sum game:f + (-f ) = 0


Life of a forward contract

K period

f

-f

Life of a forward contract

Without any loss of generality, assume an inverted market.

FT = ST

S0

F0

T: delivery date

0:Inception of contract

Life of forward contract


Payoff profit at maturity
Payoff & profit at maturity period

Payoff = Profit – price paid

Forward contract: price paid = 0

Thus: Payoff = Profit

The following terms are used interchangeably:

payoff

profit

value

gain


Payoff to the long at maturity
Payoff to the long at maturity period

Payoff at time T

= FT – K

= ST – K (FT = ST)

= fT

0

K

ST

-K


Payoff to the short at maturity
Payoff to the short at maturity period

Payoff at time T

= K – FT

= K – ST (FT = ST)

= -fT

K

0

K

ST


Zero sum game
Zero-sum game period

Payoff to the long + payoff to the short = 0

fT + (-fT) = 0

K

0

K

ST

-K


Next class
Next class period

  • Determination of forward and futures prices


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